Image reconstruction is often converted into the solution of the linear equations. In this paper

we have deduced an iterative algorithm with relaxation parameter from the successive over relaxation (SOR) method

which not only deduce the necessary of computation time and memory space but also is propitious to overcome the sensitivity of reconstructed images to incomplete noisy data. We also assess effectiveness of our algorithm by reconstruction for simulated and practical data and compare images reconstructed by filtered back projection (FBP) and the proposed method.